Generic Radiometric Dating

The simplest form of isotopic age computation involves substituting three measurements into an
equation of four variables, and solving for the fourth. The equation is the one which describes
radioactive decay:

The variables in the equation are:

Pnow - The quantity of the parent isotope that remains now. This is measured
directly.

Porig - The quantity of the parent isotope that was originally present. This is
computed from the current quantity of parent isotope plus the accumulated quantity of daughter
isotope.

halflife - The half-life of the parent isotope. Standard values are used, based on direct
measurements. (Constancy of decay rate is covered in the Age of the Earth FAQ.)

age - The value computed from the equation and the other three quantities, is the amount of
time which has passed.

Solving the equation for "age," and incorporating the computation of the original quantity of
parent isotope, we get:

Potential problems for generic dating

Some assumptions have been made in the discussion of generic dating, for the sake of keeping
the computation simple. Such assumptions will not always be accurate in the real world. These
include:

The amount of daughter isotope at the time of formation of the sample is zero (or known
independently and can be compensated for).

No parent isotope or daughter isotope has entered or left the sample since its time of
formation.

If one of these assumptions has been violated, the simple computation above yields an
incorrect age.

Note that the mere existence of these assumptions do not render the simpler dating methods
entirely useless. In many cases, there are independent cues (such as geologic setting or the
chemistry of the specimen) which can suggest that such assumptions are entirely reasonable.
However, the methods must be used with care -- and one should be cautious about investing much
confidence in the resulting age... especially in absence of cross-checks by different methods, or
if presented without sufficient information to judge the context in which it was obtained.

Isochron methods avoid the problems which can potentially result from both of the above
assumptions.

Isochron methodology

Isochron dating requires a fourth measurement to be taken, which is the amount of a
different isotope of the same element as the daughter product of radioactive decay. (For
brevity's sake, hereafter I will refer to the parent isotope as P, the
daughter isotope as D, and the non-radiogenic isotope of the same element as
the daughter, as Di). In addition, it requires that these
measurements be taken from several different objects which all formed at the same time from a
common pool of materials. (Rocks which include several different minerals are excellent for
this.)

Each group of measurements is plotted as a data point on a graph. The X-axis of the graph is
the ratio of P to Di. The Y-axis of the graph
is the ratio of D to Di. For example, an Rb/Sr
isochron plot looks like this:

P = 87Rb;
D = 87Sr; Di
= 86Sr.
Figure 1. Example isochron plot.

What does it mean?

The intent of the plot is to assess a correlation between:

The level of P (X-value of the data points), and

Any enrichment in D (Y-value of the data points):

Figure 2. Meaning of the plot axes.

If the data points on the plot are colinear, and the line has a positive slope, it shows an
extremely strong correlation between:

The amount of P in each sample, and

The extent to which it is enriched in D, relative to
Di.

This is a necessary and expected consequence, if the additional D is a
product of the decay of P in a closed system over time. It is not easily
explained, in the general case, in any other way.

Why isochron data are colinear

The data points would be expected to start out on a line if certain initial conditions were
met. Consider some molten rock in which isotopes and elements are distributed in a reasonably
homogeneous manner. Its composition would be represented as a single point on the isochron
plot:

Figure 3. Global composition of the melt.

As the rock cools, minerals form. They "choose" atoms for inclusion by their chemical
properties.

Since D and Di are isotopes of the same
element, they have identical chemical properties*.
Minerals may include varying quantities of that element, but all will inherit the same
D/Di ratio as the source material. This results in an identical
Y-value for the data points representing each mineral (matching the Y-value of the source
material).

* Note that the above is somewhat
simplified. There are minor differences between isotopes of the same element, and in relatively
rare circumstances it is possible to obtain some amount of differentiation between them. This is
known as isotope fractionation. The effect is almost always a very small departure
from homogeneous distribution of the isotopes -- perhaps enough to introduce an error of 0.002
half-lives in a non-isochron age. (It can happen... but it is rare and the effect is not large
enough to account for extremely old ages on supposedly young formations.)

In contrast, P is a different element with different chemical properties.
It will therefore be distributed unequally relative to D &
Di as minerals form. This results in a range of X-values for the
data points representing individual minerals.

Since the data points have the same Y-value and a range of X-values, they initially fall on a
horizontal line:

Figure 4. Differential migration of elements as minerals form.

A horizontal line represents "zero age." *

* More precisely, a horizontal line
represents an age which is indistinguishable from zero. In most cases, any age less than about
10-3P half-lives will include zero within
its range of uncertainty. (The range of uncertainty varies, and may be as much as an order of
magnitude different from the approximate value above. It depends on the accuracy of the
measurements and the fit of the data to the line in each individual case.) For example, with
Rb/Sr isochron dating, any age less than a few tens of millions of years is usually
indistinguishable from zero. That encompasses the entire young-Earth timescale thousands of times
over.

As more time passes and a significant amount of radioactive decay occurs, the quantity of
P decreases by a noticeable amount in each sample, while the quantity of
D increases by the same amount. This results in a movement of the data points
to the left (decreasing P) and upwards (increasing D).
Since each atom of P decays to one atom of D, the data
point for each sample will move along a path with a slope of -1.

Decay occurs in a proportional manner (that is, when 20% of the P in one
sample has decayed, 20% of the P in every sample will have decayed).
As a result, the data points with the most P (the right-most ones on the
plot) move the greatest distance per unit time. The data points remain colinear as time passes,
but the slope of the line increases:

Jon Fleming has made an
animated diagram showing the process illustrated in
Figure 5.

The slope of the line is the ratio of enriched D to remaining
P. It can be used in place of "Dnow/Pnow"
in the decay equation.

Miscellaneous notes

Age "uncertainty"

When a "simple" dating method is performed, the result is a single number. There is no good
way to tell how close the computed result is likely to be to the actual age.

An additional nice feature of isochron ages is that an "uncertainty" in the age is
automatically computed from the fit of the data to a line. A routine statistical operation on the
set of data yields both a slope of the best-fit line (an age) and a variance in the slope (an
uncertainty in the age). The better the fit of the data to the line, the lower the
uncertainty.

For further information on fitting of lines to data (also known as regression
analysis), see:

York (1969), a short technical
overview of a technique specially designed for assessing isochron fits.

Note that the methods used by isotope geologists (as described by York) are much more
complicated than those described by Gonick. This will be discussed in more detail in the section
on Gill's paper below. The "generic" method described by Gonick is easier to
understand, but it does not handle such necessities as: (1) varying levels of uncertainty in the
X- versus Y-measurements of the data; (2) computing an uncertainty in slope and Y-intercept from
the data; and (3) testing whether the "fit" of the data to the line is good enough to imply that
the isochron yields a valid age. Unfortunately, one must wade through some hefty math in order to
understand the procedures used to fit isochron lines to data.

General comments on "dating assumptions"

All radiometric dating methods require, in order to produce accurate ages, certain initial
conditions and lack of contamination over time. The wonderful property of isochron methods is:
if one of these requirements is violated, it is nearly certain that the data will indicate
the problem by failure to plot on a line. (This topic will be discussed in much more
detail below.) Where the simple methods will produce an incorrect age, isochron methods will
generally indicate the unsuitability of the object for dating.

Avoidance of generic dating's problems

Now that the mechanics of plotting an isochron have been described, we will discuss the
potential problems of the "simple" dating method with respect to isochron methods.

Initial daughter product

The amount of initial D is not required or assumed to be zero. The greater
the initial D-to-Di ratio, the further the
initial horizontal line sits above the X-axis. But the computed age is not affected.

If one of the samples happened to contain no P (it would plot where the
isochron line intercepts the Y-axis), then its quantity of D wouldn't change
over time -- because it would have no parent atoms to produce daughter atoms. Whether there's a
data point on the Y-axis or not, the Y-intercept of the line doesn't change as the slope of the
isochron line does (as shown in Figure 5). Therefore, the Y-intercept of
the isochron line gives the initial global ratio of D to
Di.

For each sample, it would be possible to measure the amount of the
Di, and (using the ratio identified by the Y-intercept of the
isochron plot) calculate the amount of D that was present when the sample
formed. That quantity of D could be subtracted out of each sample, and it
would then be possible to derive a simple age (by the equation introduced in the first section of
this document) for each sample. Each such age would match the result given by the isochron.

Contamination - parent isotope

Gain or loss of P changes the X-values of the data points:

Figure 6. Gain or loss of P.

In order to make the figures easy to read (and quick to draw), the examples in this paper
include few data points. While isochrons are performed with that few data points, the best ones
include a larger quantity of data. If the isochron line has a distinctly non-zero slope, and a
fairly large number of data points, the nearly inevitable result of contamination (failure of the
system to remain closed) will be that the fit of the data to a line will be destroyed.

For example, consider an event which removes P. The data points will tend
to move varying distances, for the different minerals will have varying resistance to loss of
P, as well as varying levels of Di:

Figure 7. Loss of P in all samples

The end result is that the data are nearly certain not to remain colinear:

Figure 8. Loss of P destroys the fit to a
line.

Even in our simple four-data-point example isochron, a change to two of the samples...

Figure 9. Migration of parent in two data points.

... would require exact changes to the remaining two samples in order for the data to remain
colinear:

Figure 10. Specific loss of P required to yield a different
colinear plot. The two samples must each change by the indicated amount -- no more and no less --
if the data are to remain colinear.

Note: In the special case where the isochron line has a zero slope (indicating zero age), then
gain or loss of P may move the data points, but they will all still fall on
the same horizontal line. In other words, random gain or loss of Pdoes
not affect a zero-age isochron. This is an important point. If the Earth were as young as
young-Earth creationists insist, then the "contamination" which they suggest to invalidate dating
methods would have no noticeable effect on the results.

Contamination - daughter isotope

In the case of Rb/Sr isochron dating, the most common form of isotope migration is a
preferential loss of radiogenic daughter (87Sr). Faure (1986, p. 123) notes:

Moreover, the daughter atoms produced by decay in a mineral are isotopes of
different elements and have different ionic charges and radii compared with their parents. The
energy released during the decay may produce dislocations or even destroy the crystal lattice
locally, thus making it all the more easy for the radiogenic daughters to escape.
[...]The observed behavior of the minerals can generally be treated as though it had been caused
solely by the migration of radiogenic 87Sr among the
constituent minerals of a rock.

This will change the vertical position of the data points:

Figure 11. Gain or loss of D.

As with gain or loss of P, in the general case it is highly unlikely that
the result will be an isochron with colinear data points:

Figure 12. Gain/loss of D destroys fit to an
isochron.

Exceptions for loss of daughter

There are two exceptions, where it is possible for migration of D to
result in an isochron with reasonably colinear data points:

If the D is completely homogenized, then the isochron age is reset to
zero. When this happens, any later dating attempt will yield the age of that metamorphic event
rather than the original time of crystallization:

Figure 13. Complete homogenization of radiogenic daughter resets the isochron age
to zero.

If the D is partially homogenized in a reasonably regular manner, the
isochron age can be partially reset and the samples will date to sometime in between the original
time of crystallization and the time of metamorphism. This is a very rare occurrence, but
examples are known:

These exceptions should be of little comfort to young-Earthers, for (1) they are uncommon
(extremely uncommon in the case of partial resetting); and (2) the result in both cases is
an isochron age which is too young to represent the time of formation. Young-Earthers
necessarily insist that all ancient isochron ages are really much too old.

So, are isochron methods foolproof?

In the real world, nothing is perfect. There are some isochron results which are obviously
incorrect. The significance of isochron plots is a bit counter-intuitive in some cases. And there
are known processes which can yield an incorrect isochron age. Does this leave room to discard
isochron dating as entirely unreliable? Not really...

The large majority of isochron dating results are in accordance with the mainstream age and
history of the Earth. If the results were essentially random numbers, that would not be the
expected distribution of results. See the tables of meteorite isochron ages in The Age of the Earth FAQ for example.

"Counter-intuitive" ages -- for example results which indicate an event earlier than
the time of crystallization of the sampled object -- are usually produced by inappropriate
selection of samples, and can be avoided in most cases. For one example, see my Critique of ICR's Grand Canyon Dating Project.

The processes which could produce incorrect isochron ages require special circumstances, and
are not universally applicable across the wide range of rock and mineral types on which isochron
dating (by several different radioactive isotopes) has been successfully performed.

Next we shall examine in detail some specific examples.

Violation of cogenetic requirement

One of the requirements for isochron dating is that the samples be cogenetic, meaning
that they all formed at about the same time from a common pool of material in which the relevant
elements and isotopes were distributed reasonably homogeneously. (As described in Figure 4, this is how the data are caused to be colinear.)

Usually it is easy to determine whether or not this requirement is met. The check is not just
the isochron plot itself (which can in most cases indicate such a problem by failure of
the data to fall on a line), but in addition the physical location and geological relationships
of the samples selected for dating.

If this requirement is violated, it is sometimes still possible to obtain an isochron plot
with reasonably colinear data points. The significance of the computed age, however, will likely
not be the last time of crystallization of each sample. It might instead be the original time at
which the samples became separated from a common pool of matter, or the age of that source
material itself. The resulting age is meaningful, but it does not have the meaning which
one might expect for the dating result (i.e., time of crystallization of the dated sample
itself).

Consider an old body of rock (as evidenced by its good fit to an isochron with distinctly
non-zero slope) with minerals which melt at different temperatures. In this example, the minerals
with the lowest melting-point having the lowest
P-to-Di and
D-to-Di ratios:

Figure 15. An old rock, minerals annotated with melting
temperatures

The rock is heated slowly, and at various times the molten portions are moved to the surface
in a series of lava flows. The earliest flows will have an isotopic composition close to that of
the minerals with the lowest melting points; the latest flows will have an isotopic composition
close to that of the minerals with the highest melting points.

The individual lava flows are not cogenetic. They did not separate at about the same
time from an isotopically homogeneous pool of matter.

For the sake of simplicity, we will assume three lava flows each with a composition matching
the data points of the previous figure:

Figure 16. The isotopic composition of the various lava flows

It is likely that at least a small amount chemical differentiation will have occurred in each
melt, and that as a result the minerals of each individual lava flow will exhibit a much younger
isochron (the actual age of each flow):

Figure 17. Mineral isochrons (red) of the various flows give several different
young ages.

The data points for the overall composition of each flow fall on an isochron line representing
the original crystallization time of the source material, which is much greater than the age of
any of the flows. This sort of inherited age is well-understood, discussed thoroughly in
the literature, and usually easily avoided by proper selection of samples.

Note also that chemical differentiation at the time of the latest melting (resulting in the
round data points in Figure 17) induces significant scatter into the isochron plot if any measure
other than whole-rock is made:

Figure 18. Data points of individual mineral samples show scatter due to chemical
differentiation at the last time of melting.

Mixing of two sources

It is also possible to obtain an isochron with colinear data, whose age has no significance
whatsoever. The only reasonably common way is by mixing of materials.

Consider two entirely independent sources of material, A and
B, each with a different isotopic composition:

Source
material

P
(ppm)

D
(ppm)

Di
(ppm)

P
---
Di

D
---
Di

A

18

37

39

0.462

0.949

B

10

17

11

0.909

1.545

Table 1. Composition of two sources

Each could be plotted as a data point on an isochron diagram:

Figure 19. Position of source material on an isochron plot.

If these sources were mixed together into a single rock, in such a way that the different
samples of the rock ended up with different proportions of A and
B, without chemical differentiation, the end result would be something like
this:

Sample
source

P
(ppm)

D
(ppm)

Di
(ppm)

P
---
Di

D
---
Di

A

18

37

39

0.462

0.949

¾ A + ¼ B

16

32

32

0.500

1.000

½ A + ½ B

14

27

25

0.519

1.080

¼ A + ¾ B

12

22

18

0.667

1.222

B

10

17

11

0.909

1.545

Table 2. Samples of a mixture, with varying portions of A and
B in each.

When plotted on an isochron diagram, the mixed data points are all colinear with
A and B:

Figure 20. Isochron plot of two mixed sources

Mixing would appear to be a pernicious problem. Since A and
B can be completely unrelated to each other, their individual compositions
could plot to a fairly wide range of locations on the graph. The line
AB could have any slope at all.

That fact also allows us to make a rough estimate of the percentage of isochrons that give
colinear plots due to mixing. "Meaningful" (or "valid") isochrons must have a zero or positive
slope; "mixing" isochrons can have any slope. If isochrons of negative slope (which
must be mixing lines) were reasonably common, then we might suspect mixing to be an
explanation for a significant fraction of all apparently valid "old" isochrons as well. That is
not the case, however.

In addition, there is a relatively simple test which can detect mixing in most cases. The test
is a plot with the same Y-axis as the isochron plot, but an X-axis of the reciprocal of total
daughter element (D + Di).

For the sample data used above, the plotted values would be:

Sample
source

P
(ppm)

D
(ppm)

Di
(ppm)

1
------
(D+Di)
(ppm-1)

D
---
Di

A

18

37

39

0.0132

0.949

¾ A + ¼ B

16

32

32

0.0156

1.000

½ A + ½ B

14

27

25

0.0192

1.080

¼ A + ¾ B

12

22

18

0.0250

1.222

B

10

17

11

0.0357

1.545

Table 3. Data for mixing plot

The resulting mixing plot looks like this:

Figure 21. Plot to detect mixing.

If the resulting data points are colinear, then the isochron is likely a result of mixing and
probably has no real age significance.

Actually the mixing data can fall on a somewhat more complicated curve. Faure (1986,
Equations 9.5 through 9.10 on p. 142) contains a precise derivation. There are simplifying
assumptions which are true in most cases and yield a line on the mixing plot.

However, when the mixing plot data fail to fall on a line:

Figure 22. Mixing plot, detecting no mixing.

... then the isochron is probably not a result of mixing, and the computed age is very
likely meaningful.

Zheng's paper

Lately it seems that some creationists have latched onto Zheng (1989), and reference this paper as if it disproved isochron dating
and made room for a young Earth. The paper is a discussion of potential problems of Rb/Sr
isochron dating, with examples of instances where these problems are known to have occurred.

However, the paper is not terribly helpful to the young-Earth cause. Zheng discusses four ways
in which an incorrect isochron could result:

Protracted fractional crystallization
Requires a slow cooling period on order of ten million years, which is not possible on a young
Earth. Also, the effect is very slight: in the only example which Zheng produces (first entry in
Table II on p. 14), the "incorrect" age (437 ± 10 Ma) is not very different from the
actual age (415 ± 10 Ma).

Inherited (for example, by partial melting)
Discussed previously; requires special circumstances and almost always induces a fair amount of
scatter in the isochron plot. Requires ancient source material (the "inherited" age matches the
age of the source), which is not available on a young Earth.

Mixing isochron
Discussed previously; in most cases detected by the mixing plot test.

Apparent isochron by metamorphism
Discussed previously; requires special circumstances and results in an age in between original
time of crystallization and the metamorphic event that partially reset the isochron. Requires
ancient source material, which is not available on a young Earth.

While each of these processes can be invoked to explain a few confusing or conflicting dating
results, none could reasonably be expected to account for all (or even most) isochron dating
results which are incompatible with a young Earth.

Summary of isochron problems

There are known processes which can result in incorrect isochron ages, and examples of each
are known in the field. If one were to assume that a good-fitting isochron implies a reliable
result, one would be correct approximately nine times out of ten. However, accuracy can be
improved further with...

Additional tests on the same data involved in the isochron plot (such as that for
mixing).

Cross-checks between different isotopes with different chemical properties.

Attention to the geologic setting from which the samples were obtained.

As Brent Dalrymple said:

Most [inaccurate ages] are caught by appropriate safeguards, like standards
and repetition, but some go unrecognized until long after the data have been published. In short,
radiometric dating methods give reliable results most of the time, but not always. [...]
With sufficient cross checks, care and experience, we don't really get fooled very often and when
we do it is usually not for long. (1992, p. 1)

Gill's paper

Recently Gill (1996) has published in
the creationist technical literature, claiming that all Rb-Sr isochron ages can be explained away
as meaningless "false" correlations. The abstract reads:

A mathematical answer is presented for the frequent occurrence of false of
"fictious" Rb-Sr isochrons. The reason for these inconsistencies is that a simple linear
regression procedure is mathematically invalid if two or more independent variables influence a
single dependent variable. In many data sets for the "isochron" procedure, there are two
independent variables involved. First, there is the desired radioactive relation between the
amount of the rubidium parent and the strontium daughter. Second, since the atomic strontium
concentration in the samples is a variable, then the isotopic Sr-87 content of the atom [sic]
is also a variable. In such a situation, the "Isochron" regression is mathematically invalid,
so both its slope and intercept are erroneous.

I recommend that interested parties obtain and read this paper. I see four major problems with
the creationist claims -- sufficient to invalidate the creationist paper rather than (as
Gill desires) the Rb-Sr dating procedure.

1. Mathematics versus chemistry:

The behavior of isochron data is constrained in two ways -- both by what is mathematically
possible on the plot, as well as by what is physically possible given the chemistry of the
relevant elements. Gill's theoretical treatment concentrates solely on mathematical behavior,
while ignoring the underlying chemistry. It therefore runs the risk of reaching false conclusions
by assuming behaviors which are mathematically possible -- but chemically unlikely or
impossible.

Gill's paper does make this sort of bad assumption: that
86Sr and 87Sr concentrations are
essentially independent:

No such simple relationship exists when the divisor [86Sr]is a variable. [...]
Once the division by a variable is done for the input to the regression, the error is
unpredictable and irrevocable.

That is the linchpin of Gill's argument. If that assumption is not accurate, then Gill's
argument falls apart. As discussed earlier in this FAQ, isotopic homogenization occurs in molten
rock (and even at temperatures short of melting in many cases) where the relevant elements
migrate freely. Once homogenization has occurred, the quantities of 86Sr and 87Sr are no longer independent
and cannot be made so.

2. Percentage of problematic Rb-Sr ages:

Gill suggests that a large percentage of Rb-Sr isochron ages are incorrect even from
mainstream science's point of view:

The geological literature is filled with references to Rb-Sr isochron ages that
are questionable, and even impossible. Woodmorappe (1979, pp. 125-129) cites about 65 references
to the problem. Fause (1977, pp. 97-105) devotes his chapter seven to possible causes of
"fictitious" isochrons. Zheng (1989, pp. 15-16) also cites 42 references.

Gill's allegations are untrue. False isochrons due to mixing may be somewhat common
(incidentally, that is the real topic of Faure's chapter seven). However, these can be (as
discussed in the mixing section of this FAQ) detected easily and eliminated
from consideration. Of the remainder, however, the overwhelming majority are well-aligned with
the results that would be expected given the mainstream age and history of the Earth.

A very large number of Rb/Sr isochrons have been performed. We cannot be impressed by numbers
of supposed bad dates in the low tens; they represent a tiny fraction of the reported results,
and (in both creationist and non-creationist papers on potential problems with the method)
represent only the "anomalous" values collected from a much larger body of data. Some of
the papers include obvious cases of mixing as well as cases where the data set is too small or
too ill-fitting to be taken seriously.

In order to perform a reasonable assessment of the percentage of Rb-Sr isochron ages which are
"inconvenient" to mainstream science, we would count those which: (1) do not fail the test for
mixing, (2) include more than four data points, and (3) show an excellent correlation (say, an
age uncertainty of less than 0.1Ga is computed from the data). It would be impractical to attempt
such an exercise on all of the Rb-Sr isochron ages that have ever been reported. However, it is
quite possible to fully examine the literature of some sub-set of the data.

Brent Dalrymple (1991, Chapters 5 and 6) reports a large number of Rb-Sr isochron ages for
meteorites and Moon rocks. These are fairly good candidates for such a survey, because: (1) they
tend to have geologically simple histories, and therefore the interpretation of the results is
more straightforward; (2) there aren't large quantities of these objects to be dated (this makes
a survey of the data easier, and also eliminates the common creationist claim that there might be
a much larger number of "inconvenient" results that are not published).

3. Gill's example is contrived:

Much of Gill's paper discusses a single example, which is contrived. He translates four
colinear data points in such a a way that the leftmost two are crowded down 3/4 of the way
towards the origin, and the rightmost two are crowded down 1/2 of the way towards the origin.

The result is essentially two "groups" of data (the point of a pair are moved closer together
by Gill's translation). Since any two things will be colinear, the two groups are colinear. Since
the data points in each group are fairly close to each other, there's not much scatter about the
line. However, had Gill chosen to divide the first and last points by four (instead of the
first two), or chosen four different divisors, the fit to a line of his changed would be much
worse than the original fit.

4. Gill ignores the isochron assessment techniques actually in use:

Gill's simple linear regressions are not the exact the technique used to assess isochron fits.
There are fairly complex means of assessing the fit versus the expected errors of measurement;
even when ("by eye") the data appear to be fairly colinear, it does not mean that the procedure
will indicate a likely valid isochron.

It's difficult to assess Gill's own example as if it were realistic, because his values are
not real isotope measurements and are just pulled out of thin air. While a correlation of 0.993
may sound impressive, several example isochron diagrams pulled out of the technical literature
had much better fits (0.997 to 0.998).

Some talk.origins questions

The following are interesting questions that were asked in talk.origins about isochron dating.
The names of the "questioners" have not been included because permission to use their names has
not been obtained.

How do you tell the difference between radiogenic and
non-radiogenic 87Sr?

For the Rb/Sr isochron method, the ratio of 87Sr to
86Sr at time of formation is not needed as an input to the
equation. Instead, it is given by the Y-intercept of the isochron line. It is a by-product of the
age computation... provided that the data are colinear.

What is isochron dating? a method, an equation, a graph ...?

An "isochron" is a set of data points in a plot which all fall on a line representing a single
age ("isochron" comes from: "isos" equal + "chronos" time). The term "errorchron" has been coined
for a set of data which are not colinear. The best-fit line itself is also sometimes
called an "isochron." The plot on which these data points appear is sometimes called an "isochron
diagram" or "isochron plot."

A dating method which uses such a plot to determine age is called an "isochron dating method."
When "isochron dating" is mentioned in this FAQ, the intent is to cover the methodology which is
common to all "isochron dating methods."

Isochron methodology is applied with the following isotopes:

P

D

Di

half-life (*109 yr)

87Rb

87Sr

86Sr

48.8

40K *

40Ar

36Ar

1.25

147Sm

143Nd

144Nd

106

176Lu

176Hf

177Hf

35.9

187Re

187Os

186Os

43

232Th *

208Pb

204Pb

14

238U *

206Pb

204Pb

4.47

* Most dating with these isotopes is not
performed via the exact isochron methodology described here.

Table 4. Isotopes used for isochron dating

How is the half life of an element determined? For something that
takes 60 billion years to partially decay, how is an exact measure of the decay rate determined
in a few hours?

Half-life assessments don't necessarily take only "a few hours." Davis et al. (1977) measured the decay rate of
87Rb (48.9 ± 0.4 billion years) by counting the
accumulation of 87Sr over a period of nineteen years.

The statistical uncertainty in an assessment of decay rate is a function of the number of
decays counted. "A few hours" (on order of 10-15 half-lives of
a long-lived isotope) is a relatively short span of time, but this is more than compensated by
the fact that even a milligram of any relevant radioactive isotope contains at least 1018 atoms.

Even in a small sample of a long-lived isotope, there will be a constant stream of decays. If
the sample's size can be measured accurately, and the number of decays can be counted accurately,
then the half-life can be computed accurately. That's the basis for the "direct counting
experiments" from which half-lives are calculated.

The line is telling us that no matter what size sample we take we
always have the same ratio of parent to daughter. [...]
So let's say that when the rocks were formed, certain amounts of both the parent and daughter
were present. But in the process of forming, everything got evenly distributed. You would get
your nice straight isochron line, but still not know the age of your sample.

The assertion would be correct if the isochron plot were quantity of parent
(P) versus quantity of daughter (D). But the graph is
instead P/Di vs
D/Di. Since Di
will vary over different minerals, the isochron data can plot on a line when
P vs D would not.

It's easy to understand how different minerals in a rock could get different
P/Di ratios. P and
Di have different chemical properties. P will
fit better into some minerals than Di (and vice versa). This
explains why data points don't all fall on the same X-value.

However, it's less easy to understand how different minerals in a rock could end up with
different D/Di ratios. What the isochron plot
can discover, if the result is a good fit to a line with positive slope, is that there is an
extremely strong correlation between (1) enrichment in D, and (2) level of
P. Since D is produced from P by
radioactive decay, the correlation strongly suggests both (1) the age of the sample and
(2) that it has been relatively free of contamination since formation.

If an area is homogeneously mixed, then you will always get the
same ratio of everything you grab. And they will all be equally related to each other. [...]
In a few thousand years the decay is insignificant, so the isochron line would just represent
uniform mixing during formation.

The situation which you describe wouldn't result in an age. If there were no chemical
separation of P vs (D and
Di) at time of formation, then all plotted data will fall on a
single point on the isochron diagram. (That point would initially be the composition of the
source material, as in Figure 3.) No best-fit line can be derived from a
single point and therefore no age would result.

But when scientists get data for something that appears
contaminated, what do they do with it? If data does not conform to the isochron method and fall
along a line it is interpreted as contamination, I presume, as your FAQ also says. Why keep
around bad samples?

It sounds as if you are suggesting that geologists might keep trying isochron plots on a
single item until they get one where the data points line up, which probably isn't representative
of its "real" age, and only that one gets published. (This is about one pace away from some
pretty heavy-duty "conspiracy-theorizing.") Here are some reasons why I strongly doubt that this
is done:

It is recognized as being dishonest. If a geologist were to plot 30 data points, and then
bury the ten which fell furthest from the least-squares-fit isochron line, the next person to
attempt to replicate the experiment would uncover the fraud. The same would be true of someone
who buried evidence of many bad plots in favor of one good one.

Outlying data points regularly reported, almost always plotted on the isochron diagram... but
occasionally not included in the computation of the best-fit line. (However this is always
made clear in the paper; exclusion of a small percentage of outliers is a reasonably standard
statistical practice for improving accuracy of calculations.)

Performing multiple isochron plots in search of a "good" one would be outlandishly expensive.
Just a single isochron age requires a fairly large number of measurements involving rather
expensive equipment. According to ICR fund-raising literature of several years ago, they spent
tens of thousands of dollars on their "Grand Canyon Dating Project" -- and had one Rb-Sr
isochron age (and some measurements of other isotopes) to show for it. (While that is a bit
extreme, it is not an inexpensive procedure.)

Further tests would likely give the same result as the first, and there would be a very low
probability of getting a significantly better plot. Most scientists would direct their attention
elsewhere (perhaps selecting a different dating method, or looking for less disturbed samples of
the same formation), rather than trying the exact same thing again.

Negative results are regularly published. Even when the plot does not yield the age directly,
it is often possible to ascertain a lot useful information about the history of the sample from
the data. For example, see Faure (1986, p.
126).

Finally, and most importantly... if it were the case that isochron ages were essentially
random, fictitious numbers, then we would not expect any sort of agreement between different
methods, results published by different researchers, etc. For example, see the tables of
meteorite isotope ages in The talk.origins Age of the
Earth FAQ. Several different investigators using several different dating methods
consistently produce concordant results.

This is easily explained (indeed, required) if these methods yield accurate ages. How is it
explained if the "ages" are essentially random numbers? Suppose that the first researcher
publishes an age of X years. Do you think that the next person to study the
same formation is going to keep repeating the isochron method until obtaining isochron data that
both plot as a line and agree with the original researcher's work? It's not his problem if
the originally published age is incorrect.

Further Reading

An excellent semi-technical introduction to isotope dating methods (with an emphasis on
isochron and Pb isotope dating) is available in Dalrymple (1991). I highly recommend this text. It is accessible to
those who haven't studied the field, and has even received reasonably positive review in
creationist literature. Isochron methods are introduced in a section titled "Age-Diagnostic
Diagrams" (pp. 102-124).

For those who don't mind wading through a college-level textbook on isotope dating, I also
highly recommend Faure (1986). It is
the standard text on the entire field, and includes a large number of references to the
primary literature. And, like Dalrymple's book, it has also received reasonably positive review
in creationist literature. Isochron methods are first introduced in Chapter 6 (specifically pp.
72-74). More detailed treatment is given in Chapter 8, and Chapter 9 is an extended treatment on
mixing.